Problem: Solve for $x$ and $y$ using substitution. ${6x+3y = -6}$ ${y = x+7}$
Since $y$ has already been solved for, substitute $x+7$ for $y$ in the first equation. ${6x + 3}{(x+7)}{= -6}$ Simplify and solve for $x$ $6x+3x + 21 = -6$ $9x+21 = -6$ $9x+21{-21} = -6{-21}$ $9x = -27$ $\dfrac{9x}{{9}} = \dfrac{-27}{{9}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = x+7}\thinspace$ to find $y$ ${y = }{(-3)}{ + 7}$ $y = 4$ You can also plug ${x = -3}$ into $\thinspace {6x+3y = -6}\thinspace$ and get the same answer for $y$ : ${6}{(-3)}{ + 3y = -6}$ ${y = 4}$